Application of Singular Perturbation Theory to the Control of Flexible Link Manipulators

Abstract

The control problem for robotic manipulators with flexible links is considered in this paper. The dynamic equations of motion can be derived by means of a recently developed Lagrangian-assumed modes method. In the case of flexibility at links it has been shown that there is no analogue of the well established computed torque method widely adopted for rigid arm control. Under the assumption that the flexible dynamics is faster than the rigid dynamics, singular perturbation theory provides an engineering tool for reduced order modeling. The resulting slow subsystem allows the determination of a tracking control as for rigid manipulators, since the number of control variables equals that of control led variables. For the fast subsystem an additive control is in charge of stabilizing the deflections along the joint angle trajectory. The result is a composite control strategy which combines the advantages of rigidity ("controllability") with those of flexibility ("lightweight compliant structures").